Traditional approaches to distributed problem solving have treated the problem as one of distributed search. In this paper, we propose an alternative, logic-based view of distributed problem solving, whereby agents cooperatively solve problems by exchanging information in order to derive the solution to a problem using logical deduction. In particular, we give a knowledge theoretic model of dis...

Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of these functions is proposed, and some algebraic properties of effectivity functions such as congruences are investigated. The relationship to stochastic rela...

Herewith a fairly old concept is published first time and named “Lucas-Interpretation”, which has been implemented in a prototype, which has been proved useful in educational practice and which gains academic relevance with an emerging generation of educational math assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction is the appropriate techn...

Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive (mythological) thinking and the second one as the toy model of everyday human reasoning in which aside from logical deduction, heuristic elements and beliefs also play ...

In this paper we will investigate which fuzzy/linguistic rules are redundant in systems of such rules called linguistic descriptions. We present a formal definition of redundancy and show that rules which are seemingly redundant can be in fact indispensable. These results apply for IF-THEN rules which use evaluative linguistic expressions (e.g., small, very big, etc.) and inference method calle...

Superdeduction is a formalism closely related to deduction modulo which permits to enrich a first-order deduction system—such as natural deduction or sequent calculus— with new inference rules automatically computed from the presentation of a theory. We give a natural encoding from every Pure Type System (PTS) into superdeduction by defining an appropriate first-order theory. We prove that this...

It is believed in the West that logic began with Aristotle, and that logic is universal. The core of Western thought—including present-day formal mathematics and the philosophy of science—is premised on the belief that logical truths are universal, that they are necessary truths, and that logical deduction is certain and infallible. These beliefs about logic however are untenable, both historic...

We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for high-level natural deduction proofs that may be written in a human-readable fashion. Setting out from a few basic logical concepts of the underlying meta-logical framework of Isabelle, such as higher-order unification and resolution, calculational commands are added to the basic Isar p...

Business Processes for Web Services are the new paradigm for the lightweight integration of business from different enterprises. Yet, there is not a comprehensive proposal for a logical framework for access control for business processes though logics for access control policies for basic web services are well studied. In this paper we propose a logical framework for reasoning (deduction, abduc...

A logical framework consisting of a polymorphic call-byvalue functional language and a first-order logic on the values is presented, which is a reconstruction of the logic of the verification system VeriFun. The reconstruction uses contextual semantics to define the logical value of equations. It equates undefinedness and nontermination, which is a standard semantical approach. The main results...